# LCP

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I intend to buy books to understand Mathematical Programming. Is there any that you guys would recommend? Thank you!

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Do you mean numerical math, or symbolic math? Geometric specific or just math in general? Differential equations (ODE or PDE)? What is your education level? (All these questions help to recommend appropriate books!)

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While I agree that "Mathematical Programming" is very ambiguous, the most beautiful and most mathematically-precise programming language in my opinion is Scheme or Lisp. Many introductory computer science textbooks utilize these languages due to this feature, and since they require you to think very differently than in a standard (procedural) language, I think the experience is very worthwhile! I don't have any recommendations, but if you're interested in a book on a certain topic I do recommend looking for highly-rated books on Amazon.com.

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"Mathematical programming" is a term that refers to the optimization (maximization or minimization) of a function with regards to a set of constraints. Depending on what constraints we put on the function and on the constraints themselves, we talk about different types of mathematical programming. For example "linear programming", "quadratic programming", and "nonlinear programming" all refer to different subsets of the problems referred to under the 'umbrella term' of mathematical programming.

Is this the "mathematical programming" you are asking about? (Considering you put "LCP" in the title of your post, I assume it is).

If so, I'm afraid I don't know of a good book that covers the whole gamut of mathematical programming. However, for practical applications to games and computer graphics you probably want to limit yourself to linear, quadratic, and convex programming. For those, I have some book recommendations halfway down this page:

Recommendations for books on linear and quadratic programming

However, none of these books talk about LCP in particular. If you're interested in LCP specifically, there's an online book available here

Morty and Yu, "Linear Complementarity, Linear and Nonlinear Programming" (Internet Edition)

that deals with the topic.

Hope this helps!

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Christer Ericson, you're right. I had spent several hours before that coding a collision detector that I had never bothered to see my question as programming numerical methods. Anyhow I'm interested in understanding the Linear Complimentary Problem. I have some idea of linear programming, for basic optimization questions (based on simplex method or the interior point algo). Thanks for the links. I'll look through it now. Anyhow I wld like books that also has solutions available either online or within the book itself as I have to learn everything on my own. Thanks!

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Christer Ericson, I went through your links & downloaded the book on convex optimization and another one on LCP that you recommended. The ebook on LCP is in postscript format which has been compressed a .tgz file. I'm using a windows system with WinRar. As such I can extract the postscript files but cannot view it. Right now I'm looking into solving through google. I dont anticipate any problem here. Thanks for all your help guys!

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More references (some of these may have been in Christer's list, I'm not sure):

1. Dave Eberly, 'Game Physics', chapter 7
2. Accompanying source code on Magic Software site
3. Doom 3 sdk (if you want to see some production LCP code)

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Quote:
 Original post by jykMore references (some of these may have been in Christer's list, I'm not sure):1. Dave Eberly, 'Game Physics', chapter 72. Accompanying source code on Magic Software site3. Doom 3 sdk (if you want to see some production LCP code)

Thanks for the jyk. Anyway for your information:

I got my inspiration to implement LCP for Dave Eberly's Game Physics. Chapter 5.2 covers the use of LCP to prevent inter-penetration. Chapter 7 covers LCP yes. Personally I find it woefully inadequate. The book itself is excellent. I just want more material on optimization theory.

As for production LCP code, I'm not so interested (for now). Presently I'm leaving the processor to do low-level optimization as I'm not familiar with the various SSEs & MMXs. My primary goal in wanting to understand LCP at fundamental levels is for optimization purposes. I have the SDK though I dont play doom 3 :-)

Update: This is (for now) a hobby. I hope there wont be any issue about me asking for solutions for the books (see the above posts). Gamedev.net did an article on Singapore (http://www.gamedev.net/reference/business/features/gameport3/page2.asp). The 2nd paragraph of the above page mentions about able-bodies men having to serve National Service. My conscription period is going to end next month (March). A few months after that I'll be enrolling in a local uni. During the intermediate period (between being discharged from service & enrolling) I have a few months to learn whatever I want to. But I have to pick it up on my own. Hence I need the solutions... Also, more suggestions for book would be useful, on say computational geometry (with solutions preferably). Lately I bought a few books which were quite crappy as they either did not have the solution manual or the book had too many mistakes. Hence I decided to check with you guys what are the better books out there before I buy it.

Thanks again!

Anis

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